Question number: 18

Describe in Detail

Prove that the number of basic variables is a balanced transportation problem is at most , where m is the number of origins and n is the number of destinations.

Explanation

First note that there are in all m + n constraints. We shall show that one of these is redundant so that there are in effect equation in mn variables and hence at most basic variable are there. We note

Question number: 19

Describe in Detail

What are control charts for variables? Find 3- σ control limits on the chart. If we are given that μ=15.95 σ=0.14 and n = 4 construct control limits for ?

Explanation

Control chart for variables are used to monitor characteristics that can be measured, e. g. length, weight, diameter, time etc. When a record is made of an actual measured quality characteristic like dimension expressed as hundredths of a millimeter, the quality is expressed by variables. For quality control of such data, two types of control chart